Epidemiological Modeling of Seasonal Influenza Through Periodic Mean-Reverting Stochastic Processes

In seven seasons of weekly Texas influenza surveillance data, diffusion exponent p = 1/2 gave the lowest direct-model RMSE 712.8 and AIC 5383.0, while p = 1 minimized stochastic SEIR RMSE 0.02926.

• Why it matters: Seasonal influenza’s annual cycle is obscured by changes in epidemic size and timing, so flexible stochastic models are needed to capture variability without overfitting.
• What they did: The authors fit periodic mean-reverting SDEs to imputed weekly surveillance data, testing p = 1/2, 2/3, 5/6, and 1, and estimated parameters via least squares/approximate maximum likelihood for direct models and sample-proportion weighted least squares for stochastic SEIR.
• The result: Deterministic SEIR estimated R = 1.158, transmission peaked about 10 weeks before infectious prevalence, and bootstrap showed dependence between mean-reversion and diffusion parameters, implying diffusion structure should match the modeled epidemiological quantity.

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